Is there anything permanently constructed at the exact point of the geographic South pole?
Yes and no. There’s the South Pole station, which is an international research outpost, and is located roughly at the South Pole. See: http://personal.ecu.edu/johnsonje/spole.htm and http://www.southpolestation.com/ for details.
At the exact spot of the South Pole, there is a marker but no buildings, see the last pic (not animated gif) from the first link. Also, because the ice on Anarctica moves, they have to relocate the marker every year, see the 2nd last Q and A from http://astro.uchicago.edu/cara/southpole.edu/qanda/qa_travel.html .
Google south pole station marker for a whole bunch of links!
Beaten during preview! Well, I’m not going to preview this one, so, a bit more detail on the marker: http://www.southpolestation.com/pole/survey.html
Yes, but yours was much more comprehensive. My hat is off to you sir.
How far does the South Pole marker drift every year?
A related question: it’s often noted in Antarctica trivia that it is the highest continent (in terms of mean altitude) due to the thickness of the icecap, beating out Asia and South America. Is there information available on what would be its status without the icecap (presumably taking post-glacial rebound into effect)? Is it largely high plateaux beneath the ice, or more similar to Australia, North America, etc., with a mix of lowland and highland areas?